Determining the flow-related cap deformation of Taylor droplets at low Ca numbers using ensemble-averaged high-speed images

Helmers, Thorben; Kemper, Philip; Thöming, Jorg; Mießner, Ulrich

doi:10.1007/s00348-019-2757-7

Cited by 8 publications

(11 citation statements)

References 47 publications

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“…At the droplet's back cap the interface is initially pulled outwards behind the gutter exits and wall-film regions and subsequently compressed at the tip. Both qualitative results correspond to the cap deformation described by the experimentally derived correlation of Helmers et al (2019a).…”

Section: Pressure Difference On the Droplet Interfacesupporting

confidence: 82%

Reconstruction of the 3D pressure field and energy dissipation of a Taylor droplet from a $$\upmu$$PIV measurement

et al. 2021

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In this study, we reconstruct the 3D pressure field and derive the 3D contributions of the energy dissipation from a 3D3C velocity field measurement of Taylor droplets moving in a horizontal microchannel ($$\rm Ca_c=0.0050$$ Ca c = 0.0050 , $$\rm Re_c=0.0519$$ Re c = 0.0519 , $$\rm Bo=0.0043$$ Bo = 0.0043 , $$\lambda =\tfrac{\eta _{d}}{\eta _{c}}=2.625$$ λ = η d η c = 2.625 ). We divide the pressure field in a wall-proximate part and a core-flow to describe the phenomenology. At the wall, the pressure decreases expectedly in downstream direction. In contrast, we find a reversed pressure gradient in the core of the flow that drives the bypass flow of continuous phase through the corners (gutters) and causes the Taylor droplet’s relative velocity between the faster droplet flow and the slower mean flow. Based on the pressure field, we quantify the driving pressure gradient of the bypass flow and verify a simple estimation method: the geometry of the gutter entrances delivers a Laplace pressure difference. As a direct measure for the viscous dissipation, we calculate the 3D distribution of work done on the flow elements, that is necessary to maintain the stationarity of the Taylor flow. The spatial integration of this distribution provides the overall dissipated energy and allows to identify and quantify different contributions from the individual fluid phases, from the wall-proximate layer and from the flow redirection due to presence of the droplet interface. For the first time, we provide deep insight into the 3D pressure field and the distribution of the energy dissipation in the Taylor flow based on experimentally acquired 3D3C velocity data. We provide the 3D pressure field of and the 3D distribution of work as supplementary material to enable a benchmark for CFD and numerical simulations. Graphical abstract

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Section: Pressure Difference On the Droplet Interfacesupporting

confidence: 82%

Reconstruction of the 3D pressure field and energy dissipation of a Taylor droplet from a $$\upmu$$PIV measurement

et al. 2021

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“…At the location of the annular stagnation region, the outer vortices attach to (droplet front) or detach from (droplet back) the interface. Here, the hydrodynamic forces of the flow interact strongly with the interface to deform the droplet (Helmers et al 2019a). The corner of both outer stagnation regions marks the entrance of the gutter, where continuous liquid bypasses the droplet.…”

Section: Stagnation Regionsmentioning

confidence: 99%

µPIV measurement of the 3D velocity distribution of Taylor droplets moving in a square horizontal channel

et al. 2020

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This paper presents a µPIV measurement of the 3D2C velocity distribution of Taylor droplets moving in a square horizontal microchannel at Ca c = 0.005 and Re c = 0.051. We reconstruct the third velocity component and present an accuracy assessment of the reconstruction based on a volume flow balance of the 3D3C velocity field. The velocity field allows the investigation of the 3D flow features such as stagnation regions and the shear rate distribution. The maximum shear rate is located at the entrances and exits of the wall films and at the corner flow (gutter) bypassing the Taylor droplet. The regions of high strain correspond to the cap positions of the Taylor droplets. An experimental data set allows visualization of the streamlines of the velocity distribution on the interface of a Taylor droplet and to directly relate it to the main and secondary vortices of the droplet phase velocity field. The measurement data are provided as a digital resource for the validation of numerical simulation or further assessment.

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“…The bypassing gutter flow is calculated based on the counterplay of this driving force, the gutter length and a viscosity correlated resistance factor β. The local droplet curvature at the gutter entrances is derived with an analytical interface shape approximation [23] and a correlation for the droplet cap curvature based on the Ca-number from our previous work [24]. The model is successfully validated by high-speed camera measurements.…”

Section: Arxiv:190502811v1 [Physicsflu-dyn] 7 May 2019mentioning

confidence: 99%

“…11. In previous work [24], we introduce a quantification of the droplet cap deformation with an elliptic approximation of the cap outline…”

Section: Model Specificationmentioning

confidence: 99%

Modeling the Excess Velocity of Low-Viscous Taylor Droplets in Square Microchannels

Helmers

Kemper

Thöming

et al. 2019

Fluids

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Microscopic multiphase flows have gained broad interest due to their capability to transfer processes into new operational windows and achieving significant process intensification. However, the hydrodynamic behavior of Taylor droplets is not yet entirely understood. In this work, we introduce a model to determine the excess velocity of Taylor droplets in square microchannels. This velocity difference between the droplet and the total superficial velocity of the flow has a direct influence on the droplet residence time and is linked to the pressure drop. Since the droplet does not occupy the entire channel cross section, it enables the continuous phase to bypass the droplet through the corners. A consideration of the continuity equation generally relates the excess velocity to the mean flow velocity. We base the quantification of the bypass flow on a correlation for the droplet cap deformation from its static shape. The cap deformation reveals the forces of the flowing liquids exerted onto the interface and allows estimating the local driving pressure gradient for the bypass flow. The characterizing parameters are identified as the bypass length, the wall film thickness, the viscosity ratio between both phases and the Ca-number. The proposed model is adapted with a stochastic, metaheuristic optimization approach based on high-speed camera measurements. In addition, our model is successfully verified with published empirical data.

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Determining the flow-related cap deformation of Taylor droplets at low Ca numbers using ensemble-averaged high-speed images

Cited by 8 publications

References 47 publications

Reconstruction of the 3D pressure field and energy dissipation of a Taylor droplet from a $$\upmu$$PIV measurement

Reconstruction of the 3D pressure field and energy dissipation of a Taylor droplet from a $$\upmu$$PIV measurement

µPIV measurement of the 3D velocity distribution of Taylor droplets moving in a square horizontal channel

Modeling the Excess Velocity of Low-Viscous Taylor Droplets in Square Microchannels

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